Question

is this arithmetic or geometric
5, 8, 12.8, 20.48

Answer 1

To determine whether the sequence \( 5, 8, 12.8, 20.48 \) is arithmetic or geometric, we need to check for the respective properties of each type.

1. **Arithmetic Sequence**: In an arithmetic sequence, the difference between consecutive terms is constant. We calculate the differences:

- \( 8 - 5 = 3 \)
- \( 12.8 - 8 = 4.8 \)
- \( 20.48 - 12.8 = 7.68 \)

The differences \( 3 \), \( 4.8 \), and \( 7.68 \) are not the same, so this is not an arithmetic sequence.

2. **Geometric Sequence**: In a geometric sequence, the ratio between consecutive terms is constant. We calculate the ratios:

- \( \frac{8}{5} = 1.6 \)
- \( \frac{12.8}{8} = 1.6 \)
- \( \frac{20.48}{12.8} = 1.6 \)

Since the ratio is the same (1.6) for each pair of consecutive terms, this sequence is a geometric sequence.

In conclusion, the sequence \( 5, 8, 12.8, 20.48 \) is a **geometric sequence** with a common ratio of \( 1.6 \).